Integral Equation Methods for Scattering by Periodic Lipschitz Surfaces
In this paper we consider the two-dimensional Dirichlet and impedance boundary value problems for the Helmholtz equation, Δu + k 2 u = 0, in a non-locally perturbed half-plane with a periodic Lipschitz boundary. The Dirichlet problem arises in a study of time-harmonic acoustic scattering of an incident field by a sound-soft, non-smooth (Lipschitz) periodic surface where the total field u t (the sum of the incident field u i and the scattered field u) vanishes. The impedance problem, with the boundary condition ∂u/∂v+iλu = 0, where λ ∈ ℂ is a constant, models acoustic or electromagnetic scattering (in both polarization cases) by a one-dimensional Lipschitz periodic boundary of finite surface impedance.
KeywordsDirichlet Problem Helmholtz Equation Lipschitz Domain Scattered Field Total Field
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